Reductio Ad Absurdum

Reducto ad absurdum is Latin for "reduction to the absurd." It is a form of argument that seeks to disprove a proposition by showing that that proposition inevitably leads to an absurdity, or of proving a proposition by assuming its negation and then showing that that assumption inevitably leads to an absurdity.[1] One use is in mathematics, as will be described in greater detail below. Reductio ad absurdum should not be confused with the straw man fallacy or the slippery slope fallacy.

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In Mathematics

Reductio ad absurdum, also called "proof by contradiction" or "proof by assuming the opposite," is a method of mathematical proof. It involves assuming the opposite of what one is trying to prove, and showing that this would lead to a contradiction. It works by the law of the excluded middle. The proof typically follows this structure: